4701 (18) For example, see: H. M. R. Hoffmann, Angew. Chem., 81, 597 (1969). (19) R. M. Roberts, R. G. Landolt, R. N. Greene, and E. W. Heyer, J. Am. Cbem. SOC.,89, 1404 (1967), and references cited therein. (20) S. Inagaki, S.Yamabe, H. Fujimoto, and K. Fukui, Bull. Cbem. SOC.Jpn., 45, 3510 (1972): S. Inagaki, T. Minato, S.Yamabe, H. Fujimoto, and K. Fukui, Tetrahedron, 30, 2165 (1974): S. lnagaki and K. Fukui, J. Am. Cbem. SOC.,97, 7480 (1975). (21) J. E. Baldwin, G. Hofle, and S. C. Choi, J. Am. Cbem. Soc., 93, 2810(1971); J. E. Baldwin. A. K. Bhatnager, S.C. Choi, and T. J. Shortridge, ibid., 93, 4082 (1971). (22) L. A. Paquette and J. C. Stowell, J. Am. Chem. SOC.,93, 2459 (1971). (23) E. S.Gould, "Mechanism and Structure in Organic Chemistry", Henry Holt, New York, N.Y., 1960, p 295. (24) (a) G. M. Whitesides and D. J. Boschetto, J. Am. Cbem. SOC.,93, 1529 (1971): (b) S. E. Jacobson and A. Wojcicki, ibid., 95, 6962 (1973). (25) (a) H. E. Zimmerman and G. L. Grunewald, J. Am. Cbem. Soc., 88, 183 (1966);(b) H. E. Zimmerman and A. C. Pratt, ibid., 92,6267 (1970):(c) H. E. Zimmerman and G. E. Samuelson, ibid., 89, 5971 (1967); 91, 5307 (1969): H. E. Zimmerman, P. Hackett, D. F. Juers, and B. Schroder, ibid.. 89, 5973 (1967);93, 3653 (1971);(d) P. S. Mariano and J. K. KO, ibid., 94, 1766 (1972): (e) H. E. Zimmerman, J. D. Robbins. R. D. McKelvey, C. J. Samuel, and L. R. Sousa, ibid., 96, 4630 (1974). (f) For a review of much of the di-x-methane rearrangement literature, see S. S.Hixon, P. S. Mariano. and H. E. Zimmerman. Chem. Rev., 73, 531 (1973). (26) H. E. Zimmerman and R. D. Little, J. Am. Chem. SOC.,94, 8256 (1972); 96, 5143 (1974). (27) Reference cited in ref 13 where the two-part xa xa interaction scheme is adopted.
+
(28) (a) P. R. Story and M. Saunders, J. Am. Cbem. SOC.,84,4876 (1962): (b) R. K. Lustgarten, M. Brookhart, and S. Winstein, hid., 89, 6350 (1967); M. Brookhart, R. K. Lustgarten, and S. Winstein, ibid., 89, 6352, 6354 (1967): R. K. Lustgarten, M. Brookhart, and S.Winstein. ibid., 90, 7364 (1968). (29) S. Winstein, 0.Rev., Chem. SOC.,23, 141 (1969). (30) S. Winstein and C. Ordronneau, J. Am. Cbem. Soc., 82, 2084 (1960). (31) The barrier to the bridge flipping in 7-norbornadienyl cation is greater than 19.6 kcal/mol at 45 'C. According to the corollary the displacement of the vinylene hydrogens by electrondonating substituents such as alkoxy or amino groups, and of the C7 hydrogen by an electronaccepting substituent such as carbonyl or cyano groups, is expected to make the equilibrium geometry more distorted and to make the barrier higher. (32) Either sign of the particular MO's can be chosen in principle without changing the physical meaning, as described in the theoretical section. (33) S. Winstein, M. Shatavsky, C. Norton, and R. B. Woodward, J. Am. Cbem. Soc.,77, 4183 (1955);S.Winstein and M. Shatavsky, ibid., 78, 592 (1956); S.Winstein, A. H. Lewin, and K. C. Pande, ibid.,85, 2324(1963).
(34) (a) R. W. Hoffmann, R. Schuttler, W. Schafer, and A. Schweig, Angew. Cbem., 84, 533 (1972); (b) L. A. Paquette and M. J. Broadhurst, J. Org. Chem., 38, 1893 (1973). (35) It would be interesting to examine experimentally the bridge flipping in 9 with highly electrondemanding substituents such as cyano or carbonyl groups at the methylene carbon and with highly electron-releasing substituents such as amino or alkoxy groups at the vinylene carbons. (36) (a) S.W. Staley and D. W. Reichard, J. Am. Cbem. Soc., 91, 3998 (1969); (b) M. V. Moncur and J. B. Grutzner, ibid., 95, 6449 (1973); (c) M. J. Goldstein and S.Natowsky, ibid., 95, 6451 (1973). (37) (a) G. Wittig and E. Hahn, Angew. Cbem., 72, 781 (1960);(b) R. A. Finnegan and R. S.McNees, J. Org. Chem., 29,3234 (1964);(c) A. Streitwieser, Jr.. and R. A. Caldwell, ibid., 27, 3360 (1962); (d) G. Wittig and J. Otten, Tetrahedron Lett., 601 (1963): G. Wittig and G. Klumpp, ibid., 607 (1963). (38) R. B. Turner, J. Am. Cbem. SOC.,86, 3586 (1964); cf. R. 8. Turner, P. Goebel, B. J. Mallon, W. E. Doering, J. F. Coburn, Jr., and M. Pomerantz, ibid., 90, 4315 (1968). (39) (a) P. Ahiberg, D. L. Harris, and S.Winstein. J. Am. Chem. SOC.,92,4454 (1970);(b) J. C. Barborak, J. Daub, D. M. Follweiler, and P.v. R. Schleyer, ibid., 91, 7760 (1969);J. C. Barborak and P. v. R. Schleyer, ibid., 92, 3184 (1970); (c) J. B. Grutzner and S.Winstein, ibid.. 92, 3186 (1970). (40) L. M. Loew and C. F. Wilcox, J. Am. Chem. SOC.,97, 2296 (1975), and references cited therein. (41) T. Kaneda, T. Ogawa, and S.Misumi, Tetrahedron Lett., 3373 (1973). (42) T. Inoue, T. Kaneda, and S.Misumi, Tetrahedron Lett., 2969 (1974). (43) E. L. Allred and J. C. Hinshaw, Tetrahedron Lett., 1293 (1968). (44) (a) T. Iwakuma, 0. Yonemitsu, N. Kanamaru, K. Kimura, and B. Witkop. Angew. Cbem., 85, 65 (1973);(b) T. Iwakuma, K. Hirao, and 0. Yonemitsu, J. Am. Chem. SOC.,98, 2570 (1974). (c) The transannular 2 -t 2 cycloaddition reaction between a C=C bond and one of the C-C 0 bonds of cyclopropane ring has been observed to occur presumably via acylation on the carbonyl oxygen attached to the cyclopropane ring [E. J. Corey and R. D. Balanson, Tetrahedron Lett., 3153 (1973)].This reaction is taken as being "catalyzed" by acyl cation instead of proton. (45) x LUMO of a carbonyl compound, acrolein, has been shown by a SCF calculation to be appreciably (-5 eV) lowered through the protonation on a lone pair of the carbonyl oxygen [K. Fukui and H. Fujimoto, Nippon Kagakuseni Koen-sbu, 29, 27 (1972)l. (46) R. C. Cookson and J. E. Kemp. Chem. Commun., 385 (1971). (47) Another electronic cau$e of symmetry-disfavored 1.3-sigmatropic shift in antibisallylic systems has recently been proposed [S. Inagaki, T. Minato, H. Fujimoto, and K. Fukui, Chem. Lett., 89 (1976)l. The multicyclic interaction effect should be essentially distinguished both from the BersonSalem's "subjacent orbital" effect and from the three-system interaction substituent effect described here.
Theory and Calculation of Carbon-Nitrogen Spin-Spin Coupling Constants Jerome M. Schulman*' and Thomas Venanzi Contribution from the Department of Chemistry, City Unicersity of New York, Queens College, Flushing, New York I 1 367. Receiced October 30, 1975
Abstract: Nuclear spin-spin coupling constants for I3C and I5N are treated theoretically in a framework of coupled HartreeFock theory using localized and delocalized molecular orbitals. Calculations implemented in the INDO integral approximation i n this model have been performed for one-, two-, and three-bond couplings in some simple nitrogen-containing organic molecules. It is demonstrated that orbital and dipolar contributions are important in cyanides and nitriles, and furthermore that molecules can be divided into two classes depending on the presence or absence of lone pairs which may contribute to 'Jch.
I. Introduction As is well known,2a indirect isotropic nuclear spin-spin coupling constants result from three types of electron coupling mechanisms: ( 1 ) Fermi contact interaction between the electron and nuclear spins, JFc, (2) interaction between the magnetic field arising from the orbital motion of the electron and the nuclear magnetic dipole, .To, and (3) interaction between the nuclear and electron spin dipoles, JSd.Recently self-consistent field calculations including the effect of the "noncontact" terms, ( 2 ) and (3), for first row atoms have been made by Blizzard and Santry,2b Tow1 and S ~ h a u m b u r g ,and ~ Schulman and N e ~ t o n The . ~ latter study of CC one-bond
coupling constants found that the Fermi contact term is usually dominant and is related to the product of the hybrids in the bonding orbitals. However, the orbital and spin-dipolar terms are not necessarily negligible and in a few cases, most notably bicyclobutane (C, C3) bonds, they are actually more important than the contact term. This led to the unusual prediction of a negative value for 'Jc,c35 which has been recently confirmed by an elegant experimenL6 For CF coupling constants the orbital terms have been found to be comparable to the contact term.2b.3 The present study deals with the case of C ' 3 N 1 5coupling constants which has not been systematically studied previously and for which there are a wide variety of bonding situations,
/
Theory and Calculation of C-N Spin-Spin Coupling Constants
Schulman, Venanzi
4702 e.g., amines, amides, nitriles, isocyanides, imines, protonated nitrogen species, etc. In view of the variations in both magnitude and signs obtained even for one-bond coupling constants, the accurate calculation of J C N is an interesting problem and one which provides a stringent test of any theory of coupling constants.
in expressing the relationship between the electronic structure of a molecule and its coupling constants. The first example of a localized orbital analysis is given in section IV. Equation 4 can be rewritten in terms of the unperturbed spin orbitals, xpo, of orbital energy epo
11. Theory
The scalar nuclear spin-spin coupling constant, J A B , between spin (vectors) IA and I B is the coefficient of the interaction energy bilinear in the nuclear spins, and is given in hertz by'" EAB
+
= hJABIA. I B
(1)
+
where J A B = JAB^' JAB' JAB^^. Since E A Bis a secondorder energy it is amenable to calculation by coupled Hartree-Fock perturbation theory7 which is known to be correct through first order in correlation while containing parts of higher-order terms as ~ e l l . ~Adapting 9* the theory to the calculation of J A Bfor each of the three terms, in turn (Le., p = Fc, 0 , sd), we obtain J A Bas the sum of contributions from the N occupied spin orbitals of the system:*
Here, xio is a molecular spin orbital appearing in the zeroth order or unperturbed N-electron determinantal wave function ( N / 2 spatial orbitals are doubly occupied); xic is the firstorder perturbation correction due to the interaction, hBP, between its electron and the nuclear spin I B , which is constructed to be orthogonal to the occupied spin orbitals xio. Since the perturbations are vector operators, xic is a vector perturbed function and the factor of l/3 appearing in eq 2 corresponds to an average taken over the possible orientations of Ig in a molecule-fixed coordinate system (the contact contribution is independent of I B orientation). The three perturbing operators hBP, summed over the electrons, are
hBo = 2BhYB hBsd = 2phyB
[3(5k ' k
rkB-3LkB
(3b)
rkB)rkBrkB-5 - SkrkB-3]
(3c)
with similar expressions holding for hAP, The xlc are obtained as solutions to the set of coupled first-order (in IB) equations
( A o ( ] ) - e l o ) X , C ( l )+ (hB + W -
(xlo1h
-+ w l x l o ) )
i = 1 , 2 , ..., N where w( 1 ) is the nonlocal self-consistency operator X X ~ O=
O
(4)
\
w(1) =
c ((x,CJr12-1(1 -
J=
P12)1x,O)
1
+
(x,OIr12-~(1 - P12)1x,C))
(5)
While eq 2 involving the x I c determined from eq 4 is an expression based on delocalized orbitals it is also possible to write J A Bi n terms of a set of localized orbitals, vlo, and the coupled-perturbed counterparts, vl c, as the analogous sum9 2
( v l o IhAP.lvlC)
J A B = (3h)-I I=
I
+ complex conjugate ( 2 ' )
The qlc satisfy an equation slightly more complicated than eq 4 and although there are no reported calculations that have obtained the localized contributions directly, eq 2' is important Journal of the American Chemical Society
1 98.16 /
Only the unoccupied spin orbitals need be included in the sum since the occupied orbitals do not contribute to JAB,the denominator ( e i o - ep0)-l being antisymmetric in i a n d p . W e may further expand the xi and their perturbation corrections in an atomic orbital basis set (4u)10
where the vector coefficient D,i is given by unocc AO's
Dui = p
CupCup*Czi(eio- e p o ) - ]
0.2
the subscripts indicating electron coordinate integrations. The quantity occ
P,'
=
j= I
(Dxj*CYj
+ Cxj*Dyj)
(9)
is the vector correction to the density matrix first order in IB, and is proportional to the atomic orbital matrix element (L;lhBIz).Should an iteration scheme for the D,; converge, J A B is obtained from eq 2, 7, 8, and 9 as AO's
JAB
= (3hI-l
IU
pru'
(ZlhAlu)
(10)
Thus J A B is proportional to the product of atomic orbital matrix elements ( t IhA I u ) and ( L; I he I z ) explicitly and implicitly, respectively. That both matrix elements of h A and hB should appear symmetrically in J A Bis clear from the a priori equivalence of nuclear spins IA and IB in eq 1. While an a b initio evaluation of JAB in the present formalism is possible for small molecules] it would be quite expensive for a molecule with say six first-row atoms as in an aromatic; the corresponding calculation at an INDO level, on the other hand, is reasonably inexpensive. This method has been programmed by Blizzard and Santry2band it is equivalent, in principle, to the finite perturbation method which has been applied to the Fermi contact termI2 but not the orbital and dipolar terms. (At a more approximate level yet are calculations employing average energy denominators.) In the spirit of the differential overlap approximation only one-center integrals ( t I hA I u ) are included in the present treatment; thus @ I and @u are valences orbitals on atom A with exponents adjusted for agreement with experiment. The final expression for JAB^' contains the factor SA~(O)SB~(O), the product of valence s densities at the two nuclei. The expressions for JAB' and JAB^^ are each proportional to ( F ~ ) , c , ( ~ - ~ ) B ,the averages being over the p valence electrons. While the approximations made in employing the INDO method (i.e., differential overlap, spherically averaged two-electron integrals, and the retention of solely one-center perturbation integrals) are not negligible, it is assumed that by treating S A * ( 0 ) S B 2 ( O ) and ( r - 3 ) A ( r - 3 ) B (hereafter referred to as u and 6 , respectively) as least-squares-determined parameters the basic accuracy of the coupled Hartree-Fock theory can be recovered. I
August 4, 1976
4703 Table 1. Calculated Values for JCN (Hz) in Nitrogen-Containing Carbon Compounds"
Molecule Hydrogen cyanide Cyanide ion (1.15 A) Acetonitrile Methyl isocyanide Methylamine Pyrrole Pyridine Pyridinium ion Pyridine N-oxide Ani 1in e
Azirane (C2NH5) Formamide Formaldoxime Nitromethane Methylenimine (CH2NH)
Bond
JCN Fc
JCN'
J c N ~ ~
3.3 -0.7 3.7 3.1 24.0 -11.9 -2.7 -14.8 -0.6 -0.7 2.9 -3.2 -13.5 3.6 -4.3 -18.3 5.4 -6.2 -8.0 -0.1 -1.6 -0.7 3.7 -11.4 0.5 -17.8 -2.1
-9.4 15.8 -7.9 0.3 -6.0 0.2 0.2 0.9 -0.1 1.6 -0.1 -0.1 1.2 0.0 -0.1 1.2 -0.1 2.1 0.4 0.0 0.0 0.0 0.4 0.7 1.9 0.2 2.1
-12.7 -8.0 - 12.7 0.1 -10.2 -0.1 -0.1 0.0 -0.1 -0.3 0.3 -0.4 -0.2 0.1 -0.3 -0.8 0.5 -0.9 -0.1 -0.2 0.0 -0.1 0.0 0.0 -0.9 -0.1 -0.8
JcN(tota1) -18.8 7.1 -16.8 3.5 7.8 -11.8 -2.6' -13.9 -0.8 0.6 3.1 -3.7 -12.5 3.7 -4.4 -17.9 5.8 -5.0 -7.7d -0.3 -1.6 -0.8 4.1 10.7 1.5 -17.7e -0.8
JcN(exptl.)/ (5.9)n -17.5h 3.0h (9.1)i -10.7J -4.5k
-13.0' -3.9 0.6' 2.5 -3.9 -1 1.9' 2.0 -5.3 -15.2' 1.4 -5.2 -11.4' -2.7 -1.3 (0.3)
-
( 2.96) nr -10.5"
" The parameters employed were SC~(O)SN~(O) = 13.79a0-~and (r-3)C(r-3)N = 1.77a0-~except for CN-, CH3CN, and the CH3NC isocyanide bond where 17.08 and 15.34 were the respective values. The experimental bond length of NaCN. The experimental geometry of Nishikawa et al., J . Chem. Phys., 23, 1735 (1955), was used. The results for a planar nitrogen geometry are J F C= -13.5, Jo = 0.4, and J'd = -0.1, and for a tetrahedral nitrogen, JFC= -2.3, Jo= 0.3, and JSd= -0.1. The experimental geometry of Lister and Tyler, Chem Commun., 152 ( 1 966), was used. The corresponding one-bond terms for planar aniline are JFC= - 13.5, Jo= 0.3, and Jsd= 0.0. e This is the value obtained from 17 iterations after which divergence occurred. In general, the presence of oxygen attached to the nitrogen seems to impede convergence. f Values in parentheses are of unknown signs. For the purposes of obtaining least-squares fits the CN- and N=C constants were taken to be positive as predicted by the calculations. g G. A. Gray, Ph.D. Dissertation, University of California, Davis, 1967. W. McFarlane, Mol. Phys., 10,603 (1966). ' W. McFarlane, J . Chem. SOC.A, 1660 (1967). J I. Morishima, A. Mizuno, and T. Yonezawa, Chem. Commun., 1321 (1970). ! , L. Paolillo and E. D. Becker, J . Magn. Reson., 3,200 (1970). T. Bundegaard and H. J. Jakobsen, J . Magn. Reson., 19,345 (1975). nt R . L. Lichter, D. E. Dorman, and R. Wasylishen, J. Am. Chem. SOC.,96,930 (1974). E. D. Becker and R. B. Bradley, cited in T. Axenrod, "Nitrogen NMR", G. Webb and M. Witanowski, Ed., Plenum Press, New York, N.Y. 1972, p. 261.
'
111. Results
In analyzing the results for J C N for the molecules in Table I a and b were treated as least-squares parameters obtained by fitting the experimental IJCN values of nine carbon-nitrogen bonds. The best agreement with experiment came from treating the triple and isocyanide bonds separately so that one fit, using the multiple CN bonds of CN- and C H ~ N E Cassuming positive coupling constants and acetonitrile, furnished a = 17.08 and b = 15.34 (in a0-3)20 with a standard deviation of 1.1 Hz. For the remaining coupling constants in Table I, a and b values of 13.79 and 1.77, respectively, obtained by fitting IJCN of methylisocyanide, methylamine, pyrrole, pyridine, pyridinium ion, and aniline (six in all), were used. Here, the standard deviation was 1.2 H z (14% of the average). In all cases the experimental geometry or a close approximate was used. From the results in Table I it can be seen that the calculations correctly predict the known signs of Jc., in every case, including a wide variety of bonding situations and an appreciable range of experimental values (-18 to +9 Hz). The reasonably good quantitative agreement with experiment allows some statements to be made regarding individual terms and trends. Examination of the Fermi contact terms in Table I shows that lJFcis large and negative in the aromatics except pyridine, small and negative in methylamine, nearly zero in C N - and Schulman, Venanzi
/
pyridine, small and positive in the nitriles, and large and positive in the isocyanide bond. In acetonitrile and pyridine the calculated Fermi contact term is smaller than the orbital and dipolar terms and it is opposite in sign to the experimental value. The orbital contribution IJo is positive except for the C r N and N=C bonds and curiously, in almost all cases it has a sign opposite that of the contact term (as is the case for ' J C C as well4). IJo is the dominant contributor to J C N for CN-, which our calculation suggests is positive. The dipolar term lJsdis negligible with the exception of C=N and N=C bonds. It makes the largest contribution in CH3CN where it combines with the orbital term of like sign to give a large negative IJcN. In CH3NC and CN- 'JSd is also large and negative, although not the dominant term. Thus, it is found that within Table I there are instances in which each of the three terms may make the largest contribution to I JcN. It might also be noted that of the three terms lJFcis very sensitive to the geometry used whereas IJo and lJSdare not. An example of this are the three respective contributions to IJ for the cyanide ion a t a bond length of 1.07 A (-6.0, +12.9, and -4.1); here there is a tenfold increase in the contact term. A second example is the sensitivity of lJFcin amines to the extent of pyrimidization as evidenced from the values for methylamine at the experimental and assumed planar and tetrahedral nitrogen geometries. The effect of vibrational averaging is currently under investigation. Theory and Calculation of C-N Spin-Spin Coupling Constants
4704
In contrast to the one-bond constants, 2 J and ~ 3 ~ J are~ ~dominant. Thus substituting the nominal value of 33.3% for both carbon and nitrogen into eq 11 (Le., sp2 bonding hybrids) always dominated by the Fermi contact term. The calculated results are in good agreement with experiment except for 2 J ~ leads ~ to ~ J C of N ca. - 13 Hz, which is indeed nearly the case for pyrrole and planar aniline whose lone pairs are pure p, in pyrrole and aniline where the error in magnitude is large. Finally, Table I contains calculated coupling constants for pyridinium ion, and the predicted value for formamide (as well as the experimental values in magnitude of other amides16). several molecules for which there are no experimental results, Whether the predicted linearity will hold up awaits more realthough related systems have been studied. For the threemembered ring-molecule azirane we obtain J C N = +4.1 Hz; fined calculation of the hybrizations. a sign determination of J C N in a substituted oxazirane furIt is of interest to try to make a closer connection between the presence of a lone pair and the resultant coupling constant. nished +4.9 Hz.I4 The calculated value for JCN in formamide Thus we seek to examine the origin of lJFc from the vantage was - 10.7 Hz. As the measured magnitude of JCN in acetpoint of the localized orbital description, eq 2’. First, consider amide and similar systems is 14 Hz,I5 this result seems reathe role of the localized C N bond orbital in the sum over states. sonable and we assign their signs to be negative. The u orbital of a spin, quao, when perturbed by the operator There is no experimental value of IJCN in methylenimine s , 6 ( F ~ ) is modified by mixing in some antibonding component which, using an a b initio optimized geometry, we calculate to q,*,O. Since the carbon and nitrogen 2s coefficients are of the be -0.8 Hz. An experimental determination of IJCN has resame sign in quaoand opposite sign in qu*ao,given the negative cently been made for the syn and anti isomers of the N-terteffective energy denominator and the negative YN,quaomakes butylimine of 9-anthra1deh~de.I~ In both cases the value oba negative contribution to I J F c . A similar argument leading tained was -5.0 Hz. It seems likely that the negative sign for to a negative contribution from qopo can readily be conmethylenimine is correct. In this regard it is interesting to note structed. that a positive ~ J C is N calculated for formaldoxime due prinFor class I1 molecules, however, an additional contribution cipally to the fact that the Fermi contact term is much smaller to IJFcfrom the lone pair must be considered. At first glance (and positive) than in methylenimine. It is not clear whether it might be thought that no contribution would be made from the difference in contact terms arises from the oxygen or from qlPosince if it were fully localized on nitrogen there would be differences in geometry of the two molecules. no contact interaction with the carbon nucleus. However, the small “tail” of the lone pair on the other atoms, needed for its orthogonality to the other localized orbitals, supplies the carbon IV. Discussion density. To determine the sign of the contribution in eq 2’ of The present study supplies answers to the questions: (1) d o the lone pair one must again follow the relative signs of CzSand the orbital and spin-dipolar terms make significant contriNzs in:q and qPc.Briefly, it appears that the perturbation butions to J C N ; and (2) what is the utility and scope of the correction will be derived principally from the quio virtual Binsch relation” between ~ J C and N the product of percent s orbital as the lone pair has no antibonding counterpart. Also, characters in the bonding hybrids in the examples we have examined, 771: has oppositely signed CzS and Nzscoefficients unlike the quo case and therefore it JCN = -0.0 125ScSy (1 1) makes a positive contribution to IJFc.Of course, when the lone (minus sign supplied here)? As we have seen, the answer to the pair has no s content, no contact contribution from it exists. It first question is yes for nitriles, isocyanides and pyridine, where appears to be difficult to prove that the lone-pair contribution ‘J0and lJSdare inherently large and the contact terms are will, in general, be positive as this depends on the sign of Czs small. Also noteworthy is the fact that the contact term is in the lone pair tail which could, in principle, be influenced by frequently positive in these systems (though it is of the correct nitrogen substituents and perhaps geometry. Thus there may sign in the other couplings) and this immediately provides ultimately be found examples in which both the quo and qpo counterexamples to eq 11 whose right-hand side must be lead to negative terms in eq 2’ for an exhaltation of the Binsch negative by the definition of percent s character. In fact, there prediction. is nothing particularly anomalous about the hybridizations in T h e above argument is a qualitative interpretation of the pyridine, for example, both atoms use nearly sp2 orbitals as one-bond lone-pair effect based on uncoupled perturbation shown from a localization of the I N D O orbitals.’* W e turn theory arguments. In order to obtain a quantitative interprethen to the origin of these seemingly unusual contact terms. tation based on the coupled Hartree-Fock theory, a localized Examination of the sum over occupied molecular orbitals orbital analysis has been made for the Fermi contact term of in eq 2 shows, for pyridine, that the small value lJFc= -0.7 the one-bond constant of pyridine according to eq 2’. The second term of this equation was written in the form arises from a cancellation of terms. A large positive contribution arises from the highest occupied molecular orbital which E,( ql0lhgFc.glC)where 1 vic) is the localized coupled Hartree-Fock correction due to the perturbation hAFc. The results, is largely lone pair in character. In contrast, no such cancellation is found in the calculation of lJFcfor the pyridinium ion, given in Table 11, confirm that the net, small coupling constant the result being a large negative value. Similar cancellations lJcyFcof pyridine arises from extensive cancellation among occur for the other entries of Table I which have small contact the various terms in the sum over occupied localized molecular terms. The common feature in each of these cases is the presorbitals, the principal contributors being the localized C N u bond, the lone pair, and those localized orbitals proximate to ence of a lone pair containing s character. Thus, it appears that the CN bond. This seems physically reasonable. large negative values of lJFcoccur in molecules having no such lone pairs (class 1 molecules), while smaller negative or positive The sum of the localized orbital contributions excluding that IJFc,values depending on the extent of the cancellation, are of the lone pair is - 16.5 Hz, reasonably close to the value apfound when a u lone pair is present on the nitrogen (class I1 pearing in our discussion of the Binsch relationship vide supra, molecules) or carbon in the case of an isocyanide. This onewhile the lone pair contribution, 15.5 Hz, provides the nearly bond lone-pair effect is particularly pronounced in methylicomplete cancellation inferred previously from the delocalized socyanide where the presence of a lone pair on carbon leads to orbital resuits, according to eq 2 . It thus seems fair to speculate a large positive I J F c . that the localized contributions sans the lone pair are to some It appears that the Binsch relationship might retain its vaextent transferable within molecules of the same type bond, lidity if applied strictly to class I molecules where the canceli.e., single, double, and perhaps triple C N bonds, while the lation does not occur and the contact term is therefore also lone-pair contribution will vary independently and significantly Journal of the American Chemical Society
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98:16
/
August 4 , 1976
4105
presumably positive from the calculations reported.I9 Here the lone pair of the 2 isomer should have more p character to diminish its repulsion by the methyl group leading again to a smaller IJCNFc. Finally, the one-bond lone-pair effect can be expected to appear for nuclei other than nitrogen (e.g., P) bonded to nuclei other than carbon (e.g., H). Thus, a positive lone-pair contribution explains the anomalously small value of 'JNH observed in diphenylketimine, and an orbital mechanism need not be invoked.
Table 11. Localized Orbital Contributions to ' J c , N in~ Pyridine ~ (Hz) Localized
Contribution to 'JC,N~~
CIN Lone pair CiHi ClC2 NCS CsH5
-24.3 15.5 9.9
-4.9 2.2 0.7
Localized orbitalafb
Contribution to
c2c3 c3c4
-0.1 -0.1 0.1 -0.1 0.1 0.0
J c ,N Fc
I
C2H2 C3H3 c4cs C4H4
Total
-1.0
The orbitals, localized according to the Edmiston-Ruedenberg criterion, were of u and T symmetry; the latter make no contribution to the coupling constant. The molecular geometry was slightly different from that used for the pyridine calculation of Table I.
from case to case, disappearing to a large extent on protonation and loss of its s character. The existence of an explicit contribution to ' J c Nfrom ~ ~the lone pair allows an explanation of several observations which have appeared in the literature. For example, the oxazirane with coupling constant +4.9 is in the Z configuration with its
z
E
Rl = pnitrophenyl R, = isopropyl
CH bond and lone pair cis.14 The corresponding E isomer with lone pair andp-nitrophenyl group cis has a coupling constant of magnitude 3.1 (presumably positive). The difference in J for the two isomers could accounted for by a larger amount of p character in the E lone pair to reduce its greater steric repulsion, the result being a smaller positive contribution. Of course, a concomitant increase in the s character of the nitrogen hybrid in the CN bond would lead to the same result, and only a detailed calculation would predict which effect was the more important (and to some extent they are not independent). However, the overall net positive sign of J indicates that the ldne pair is making a contribution which is important. The same kind of argument can be made for the Z and E isomers of acetaldoxime, J = 2.3 and 4.0, respectively, and
Acknowledgments. J.M.S. wishes to thank the CUNY Research Foundation for a grant-in-aid (No. 10595) and the Alfred P. Sloan Foundation for its support. References and Notes (1) Alfred P. Sloan Research Fellow. (2) (a) N. F. Ramsey, Phys. Rev., 91, 303 (1953); (b) A. C. Blizzard and D. P. Santry, J. Chem. Phys., 55, 950 (1971). (3) A:D. C. Tow1 and K. Schaumbura. Mol. Phvs., 22, 49 (1971). (4) J. M. Schulman and M. D. Newton, J. Am. Chem. SOC., 96, 6295 (1974). (5) The customary notation uses a lefl superscript n for the coupling constant of two nuclei separated by n 1 atoms. A coupling mechanism is indicated by a right superscript, the absence thereof indicatingthe total of the three contributions is being considered. (6) M. Pomerantz, R. Fink, and G. Gray, J. Am. Chem. SOC., 98, 291 (1976). (7) P. W. Langhoff. M. Karplus, and R. P. Hurst, J. Chem. phys., 44, 505 (1966), and references therein. (8) (a) T. C. Caves and M. Karplus, J. Chem. Phys., 50, 3649 (1969): (b) J. I. Musher, ibid., 46, 3649 (1967). (9) A. T. Amos, J. I. Musher, and H. C. Ff. Roberts, Chem. Phys. Lett., 4, 93 (1969). (IO) Strictly speaking, the basis set for the constant term should be enlarged to include logarithmic terms; however, a large atomic basis may be sufficient; see J. M. Schulman and D. N. Kaufman, J. Chem. Phys., 53, 477 (1970). (11) R. Ditchfield and L. C. Snyder, J. Chem. Phys., 56, 5823 (1972). (12) G. E. Maciel, J. W. Mclver, Jr., N. S. Ostlund, and J. A. Pople, J. Am. Chem. Soc., 92, 11 (1970), and references therein. (13) Actually, the theory has as yet to be tested in an accurate ab initio caiculation of a coupling constant. The present assumption of accuracy is based on the argument that it contains the correlation contribution to JAB to first order, and to some extent, beyond. Of course, it is quite conceivable that even extended-bases ab initio SCF calculations will not always prove sufficient. (14) W. B. Jennings, D. R. Boyd, C. G. Watson, E. D. Becker, R. B. Bradley, and D. M. Jerina, J. Am. Chem. SOC., 94, 8501 (1972). The molecule studied was an oxazirane substituted on carbon with 4-nitrophenyl and nitrogen with isopropyl groups, respectively. (15) R. L. Lichter, C. G. Fehder, P. H. Patton, J. Combes, and D. E. Dorman, J. Chem. Soc., Chem. Commun., 114 (1974). (16) H. J. C. Yeh, H. Ziffer, D. M. Jerina, and D. R. Boyd, J. Am. Chem. SOC.,95, 2741 (1973). (17) G. Binsch. J. B. Lambert, B. W. Roberts, and J. D. Roberts, J. Am. Chem. SOC.,86, 5564 (1964). (18) M. D. Newton (private communication). The carbon and nitrogen hybrids in the C-B bond are sp'.' and respectively. The lone pair is S P ' . ~ . (19) R. L. Lichter, D. E. Dorman, and R. Wasylishen. J. Am. Chem. SOC.,96, 930 (1974). (20) NOTEADDEDIN PROOF. JCN for l4N=C of methyl isocyanide has recently been determined to be positive, +6.33 Hz N. J. Koole, D. Knol, and M. J. A. DeBie, J. Ma@. Reson., 21,499 (19761contrary tothe assumption made here; this requires a Mdification of a and 6 for CN triple bonds. Using the corresponding isocyanide J1sNc, -8.9 Hz, J = -17.5 Hz for acetonitrile, = 77.5 Hz for 2,4,6-trimethylbenzonitrileoxide [M. Christi, J. and JCN~ P. Warren, B. L. Hawkins, and J. D. Roberts, J. Am. Chem. Soc., 95,4392 (1973)], presumably negative, a = 13.10 and 6 = 20.85 are obtained. The four triple bond values of Table I should be so modified, leading to no change in the conclusions reached heretofore. For benzonitrile oxide, the model = -75.2 Hz arises from JFc for the latter compound, the calculated JCN = -34.4, JQ= -23.0, and JSd= -17.8 Hz.
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/ Theory and Calculation of C-N Spin-Spin Coupling Constants
